It is advantageous for many applications to provide a tunable optical filter to reflect a specific wavelength while maintaining a high spectral throughput for other wavelengths. A discrete reflection filter design may be made spatially tunable. However, a discrete reflection filter having a desired narrow reflection wavelength band, and also a high spectral throughput, may be difficult to achieve.
For example, a comb filter design exhibits only a notched spectral throughput characteristic, although the comb filter may be rotatably tunable.
Filter wheels also exhibit poor spectral throughput and also have, in general, broad spectral notches. An example of a circularly variable wide bandpass interference filter is described in U.S. Pat. No. 3,442,572, issued May 6, 1969 to R. F. Illsley et al. This filter employs a plurality of quarter wavelength thick layers of low and high index of refraction coatings.
Wedged filters are also known in the art. In U.S. Pat. No. 4,346,992, issued Aug. 31, 1982 to J. Schwartz there is described a laser detector and spectral analyzer that includes a wedge interference filter having a systematic positional variation in a thickness of deposited interference layers. This results in a systematic variation in the center of the local passband with position along a left-right axis of the filter. In U.S. Pat. No. 2,708,389, issued May 17, 1955 to F. W. Kavanagh there is described a wedged interference filter having supplementary wide passband filters. In U.S. Pat. No. 4,187,475, issued Feb. 5, 1980, to I. Wieder there is described a wedged transmission filter as an output mirror for a pulsed dye laser. In SU 1208-525-A there is described a narrow band interference filter that employs alternating layers of titanium dioxide and silicon dioxide deposited by electron beam (E-beam) evaporation.
One type of reflection filter that does exhibit a narrow wavelength reflection band, and that does not require alternating sequences of discrete quarter wavelength high and low index interference films, is known as a rugate.
In this regard reference is made to an article entitled "Spectral Response Calculations of Rugate Filters Using Coupled-wave Theory", by W. H. Southwell, Journal of the Optical Society of America, Vol. 5(9), 1558-1564 (1988). This article discusses gradient-index interference filter coatings having an index of refraction that varies in a continuous fashion in a direction normal to a substrate. A narrow bandwidth reflector is shown to be achieved with a rugate coating, the bandwidth being inversely proportional to rugate thickness.
In FIG. 1 there is shown an exemplary rugate index of refraction (n) profile as a function of mechanical thickness of the rugate coating. In FIG. 1, the filter substrate is on the right, light is incident from the left, n.sub.o is the average index of refraction through the rugate, and n.sub.1 is the peak index of refraction variation, which is typically small compared with n.sub.o.
The word rugate, when used as a noun, is herein intended to define a gradient-index interference filter whose index of refraction profile is periodic as a function of film thickness. A typical example is a sine wave. When used as an adjective, the word rugate is herein taken to describe the periodic gradient index of refraction profile of a coating.
For a single wavelength a rugate has an index of refraction (index) profile of: EQU n=n.sub.o +n.sub.1 sin(Kx+.phi.), K=2(n.sub.o)k, k=2.pi./.lambda..
where n.sub.o is an average index, n.sub.1 is a peak index variation, K determines a wavelength .lambda. for which maximum reflection occurs, .phi. is a starting phase of the index variation, and x is a thickness within a range of (0.ltoreq.x.ltoreq.L). The reflectivity (r) produced by this profile is approximated by: EQU r=tanh(u/4)exp(i.phi.) EQU u=KLn.sub.1 /n.sub.o =2.pi.Nn.sub.1 /n.sub.o,
where .DELTA..lambda./.lambda.=n.sub.1 /n.sub.o is a fractional bandwidth, where N is a number of cycles in the coating, normally half integer, and L is the physical thickness of the coating. It can be seen that the maximum reflectivity at .lambda. is determined by the product of the fractional index variation times the number of cycles.
For multiple wavelengths which are separated on the order of .DELTA..lambda., a rugate may be obtained for each wavelength by summing index profiles: EQU n=n.sub.o +.SIGMA.n.sub.i sin(Kix+.phi.i),
as is shown in FIG. 2 for rugates A, B, and C, the summation of which provides the index variation, as a function of coating mechanical thickness, shown as D. For this technique multiple reflection bands are generated by depositing a single coating layer having an index of refraction profile which is predetermined to be the sum of the periods of the desired spectral lines. This technique is known as parallel deposition. A narrow multiple reflection notch rugate filter may also be obtained by serially depositing a plurality of coatings, each having a different index of refraction profile. That is, one coating is deposited upon another. A combination of serial and parallel rugate coating deposition techniques may also be employed.
FIG. 3 graphically illustrates a transmission plot of a typical narrow notch multiple line rugate filter, and FIG. 4 graphically illustrates a corresponding optical density plot for the multiple line rugate filter of FIG. 3. Optical density (D) is defined to be the base 10 logarithm of the reciprocal of transmittance (T): EQU D=log.sub.10 (1/T), or T=10.sup.-D.
As a result of these properties, a rugate filter design may greatly extend a filter's applications, in that a rugate filter has properties of narrow, high optical density and single or multiple reflection bands which lack significant harmonic structure. The rugate property of not exhibiting significant harmonics eliminates the interaction of serially disposed subfilms, or coatings, on spectral performance. In contradistinction, harmonic reflection bands in a discrete filter subfilm, that is designed to cover a long wavelength region, may adversely impact performance at a short wavelength region.
It is thus one object of the invention to provide a rugate narrow reflection band filter wherein a wavelength of the narrow reflection band is spatially varied over the filter.